A group of small shareholders has reached a settlement with RBS over claims that they were misled about the bank's health before it asked investors for £12bn in 2008.
The 9,000-strong RBS Shareholders Action Group has confirmed that it has accepted 82p a share.
It is almost double the original offer made by RBS.
The case will now go back to the High Court on Thursday where Mr Justice Hildyard will hear if it will proceed.
The RBS Shareholders Action Group sent a letter to its members over the weekend recommending the offer - which is less than the 92p a share compensation some investors had hoped to secure.
It is also below the 200p-230p that investors paid to buy shares in the rights issue nine years ago.
"Having carefully considered the merits of the current offer... we have decided to accept the offer of 82 pence per share on behalf of our membership," the action group said in a letter dated 27 May that was published on Monday."
It added: "This is a decision which is fully supported by our legal advisers."
The settlement is worth about £200m in total.
Court case adjourned
The case had been due to start on Monday, 22 May, and had been scheduled to last for 14 weeks.
However, it was adjourned and the parties began discussions over reaching a settlement.
The dispute centres on RBS's decision, during the financial crisis, to ask shareholders for billions of pounds worth of funds after it bought Dutch rival ABN Amro.
Shortly afterwards, the government was forced to prop up the bank with £45bn of taxpayers' money to save it from collapse. The state still owns a 72% stake in RBS.
The bank and former directors deny any wrongdoing.
The bank has already settled the majority of claims over the issue, but has not admitted liability.